How to write a script which move the character when the it entered an area?

Depends on what your area is made of (terrain, mesh, 2d-graphics)

Normally this is nothing one scripts but something that is handled by the physics engine. You use colliders/controllers for that.

Example: you make a character and add component->physics->character_controller and a rigid body to it, you add a terrain-heightmap and add a component->physics->terrain_collider to it and the physics engine handles the rest.

Then you move your character NOT using transform+=x; BUT changing the velocity of it's rigid body, like this maybe:

 var Vertical: float = Input.GetAxis ("Vertical") * speed; 
 var Horizontal: float = Input.GetAxis ("Horizontal") * rotationSpeed;
 rigidbody.AddForce(Vector3(Horizontal,0,Vertical),ForceMode.VelocityChange);

Note that unity comes with prefabs for this, try this: 1. start a new scene 2. delete the main camera 3. Add Terrain->Create Terrain 4. Add A first person character controller (in the projects window standard assets/character controller/) 5. Move your first person controller so you don't fall into empty space

So you'll have a walkable terrain. Other than that I recommend taking some video lessons to get started with unity. I recommend the one http://www.vtc.com/ has put out. Or Youtube.